Matrix and Stokes vector representations of detectors for polarized waveforms: theory, with some applications to teleseismic waves

This paper deals with the problem of detecting polarized waveforms in multivariate time series. Detectors are designed in the frequency domain using the spectral matrix and matrix-algebra, and also a Stokes vector-algebra. All the detectors are expressed as functions of inner products in real vector spaces, and consequently are extremely easy to program for digital computers, and are computationally very efficient. Several suggestions for the application of the detectors to the interpretation of teleseismic waveforms are given.